Question

Salt water can be desalinated by distillation. How much energy is needed to convert 175 g of salt water at 28.0 °C to water vapor if the specific heat of salt water is 5.19 J/g K, the boiling point of salt water is 102.5 °C, and the enthalpy of vaporization is 2.26 kJ/g?
A. 317 kJ
B. 399 kJ
C. 463 kJ
D. 512 kJ
E. 673 kJ

Answer 1

Answer:

$\Delta H=4.63x10^{5}J=463kJ$

Explanation:

Hello,

In this case, we find the following states:

a. Liquid salt water at 28.0 °C.

b. Liquid salt water at 102.5 °C.

c. Vapor salt water at 102.5 °C.

The first process (1) is to heat the liquid water from 28.0 °C to 102.5 °C and the second one (2) to vaporize the liquid salt water. In such a way, each process has an amount of energy that when added, yields the total energy for the process as shown below:

$\Delta H=\Delta H_1+\Delta H_2\\\Delta H=mCp\Delta T+m\Delta _VH\\\Delta H=175g*5.19\frac{J}{g*K}*(375.65K-301.15K)+175g*2.26\frac{kJ}{g} *\frac{1000J}{1kJ} \\\Delta H=4.63x10^{5}J=463kJ$

Best regards.